I have seen this problem occasionally, and it has been discussed here. In some cases, the MacFireWall prevents the Mac from talking to the DHCP server on the router.
Turning off the Firewall can help.
Alternatively, set a manual IP address in your router's range. i.e. 192.168.1.x or 10.0.0.x, where x is a number usually between 2-15. (Subnet mask 255.255.255.0).
If that isn't sticking, then something is very wrong.
I've not seen the problem in Snow Leopard.